Dynamic trees for image modelling

This paper introduces a new class of image model which we call dynamic trees or DTs. A dynamic tree model specifies a prior over structures of trees, each of which is a forest of one or more tree-structured belief networks (TSBN). In the literature standard tree-structured belief network models have been found to produce “blocky” segmentations when naturally occurring boundaries within an image did not coincide with those of the subtrees in the rigid fixed structure of the network. Dynamic trees have a flexible architecture which allows the structure to vary to create configurations where the subtree and image boundaries align, and experimentation with the model has shown significant improvements. For large models the number of tree configurations quickly becomes intractable to enumerate over, presenting a problem for exact inference. Techniques such as Gibbs sampling over trees and search using simulated annealing have been considered, but a variational approximation based upon mean field was found to work faster while still producing a good approximation to the true model probability distribution. We look briefly at this mean field approximation before deriving an EM-style update based upon mean field inference for learning the parameters of the dynamic tree model. To whom correspondence should be addressed. 1 After development of algorithms for learning the dynamic tree model is applied to a database of images of outdoor scenes where all of its parameters are learned. DTs are seen to offer significant improvement in performance over the fixed-architecture TSBN and in a coding comparison the DT achieves 0.294 bits per pixel (bpp) compression compared to 0.378 bpp for lossless JPEG on images of 7 colours.